// Tencent is pleased to support the open source community by making RapidJSON available.
// 
// Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved.
//
// Licensed under the MIT License (the "License"); you may not use this file except
// in compliance with the License. You may obtain a copy of the License at
//
// http://opensource.org/licenses/MIT
//
// Unless required by applicable law or agreed to in writing, software distributed 
// under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR 
// CONDITIONS OF ANY KIND, either express or implied. See the License for the 
// specific language governing permissions and limitations under the License.

#ifndef RAPIDJSON_BIGINTEGER_H_
#define RAPIDJSON_BIGINTEGER_H_

#include "../rapidjson.h"

#if defined(_MSC_VER) && defined(_M_AMD64)
#include <intrin.h> // for _umul128
#pragma intrinsic(_umul128)
#endif

RAPIDJSON_NAMESPACE_BEGIN
    namespace internal {

        class BigInteger {
        public:
            typedef uint64_t Type;

            BigInteger(const BigInteger &rhs) : count_(rhs.count_) {
                std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type));
            }

            explicit BigInteger(uint64_t u) : count_(1) {
                digits_[0] = u;
            }

            BigInteger(const char *decimals, size_t length) : count_(1) {
                RAPIDJSON_ASSERT(length > 0);
                digits_[0] = 0;
                size_t i = 0;
                const size_t kMaxDigitPerIteration = 19;  // 2^64 = 18446744073709551616 > 10^19
                while (length >= kMaxDigitPerIteration) {
                    AppendDecimal64(decimals + i, decimals + i + kMaxDigitPerIteration);
                    length -= kMaxDigitPerIteration;
                    i += kMaxDigitPerIteration;
                }

                if (length > 0)
                    AppendDecimal64(decimals + i, decimals + i + length);
            }

            BigInteger &operator=(const BigInteger &rhs) {
                if (this != &rhs) {
                    count_ = rhs.count_;
                    std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type));
                }
                return *this;
            }

            BigInteger &operator=(uint64_t u) {
                digits_[0] = u;
                count_ = 1;
                return *this;
            }

            BigInteger &operator+=(uint64_t u) {
                Type backup = digits_[0];
                digits_[0] += u;
                for (size_t i = 0; i < count_ - 1; i++) {
                    if (digits_[i] >= backup)
                        return *this; // no carry
                    backup = digits_[i + 1];
                    digits_[i + 1] += 1;
                }

                // Last carry
                if (digits_[count_ - 1] < backup)
                    PushBack(1);

                return *this;
            }

            BigInteger &operator*=(uint64_t u) {
                if (u == 0) return *this = 0;
                if (u == 1) return *this;
                if (*this == 1) return *this = u;

                uint64_t k = 0;
                for (size_t i = 0; i < count_; i++) {
                    uint64_t hi;
                    digits_[i] = MulAdd64(digits_[i], u, k, &hi);
                    k = hi;
                }

                if (k > 0)
                    PushBack(k);

                return *this;
            }

            BigInteger &operator*=(uint32_t u) {
                if (u == 0) return *this = 0;
                if (u == 1) return *this;
                if (*this == 1) return *this = u;

                uint64_t k = 0;
                for (size_t i = 0; i < count_; i++) {
                    const uint64_t c = digits_[i] >> 32;
                    const uint64_t d = digits_[i] & 0xFFFFFFFF;
                    const uint64_t uc = u * c;
                    const uint64_t ud = u * d;
                    const uint64_t p0 = ud + k;
                    const uint64_t p1 = uc + (p0 >> 32);
                    digits_[i] = (p0 & 0xFFFFFFFF) | (p1 << 32);
                    k = p1 >> 32;
                }

                if (k > 0)
                    PushBack(k);

                return *this;
            }

            BigInteger &operator<<=(size_t shift) {
                if (IsZero() || shift == 0) return *this;

                size_t offset = shift / kTypeBit;
                size_t interShift = shift % kTypeBit;
                RAPIDJSON_ASSERT(count_ + offset <= kCapacity);

                if (interShift == 0) {
                    std::memmove(&digits_[count_ - 1 + offset], &digits_[count_ - 1], count_ * sizeof(Type));
                    count_ += offset;
                } else {
                    digits_[count_] = 0;
                    for (size_t i = count_; i > 0; i--)
                        digits_[i + offset] = (digits_[i] << interShift) | (digits_[i - 1] >> (kTypeBit - interShift));
                    digits_[offset] = digits_[0] << interShift;
                    count_ += offset;
                    if (digits_[count_])
                        count_++;
                }

                std::memset(digits_, 0, offset * sizeof(Type));

                return *this;
            }

            bool operator==(const BigInteger &rhs) const {
                return count_ == rhs.count_ && std::memcmp(digits_, rhs.digits_, count_ * sizeof(Type)) == 0;
            }

            bool operator==(const Type rhs) const {
                return count_ == 1 && digits_[0] == rhs;
            }

            BigInteger &MultiplyPow5(unsigned exp) {
                static const uint32_t kPow5[12] = {
                        5,
                        5 * 5,
                        5 * 5 * 5,
                        5 * 5 * 5 * 5,
                        5 * 5 * 5 * 5 * 5,
                        5 * 5 * 5 * 5 * 5 * 5,
                        5 * 5 * 5 * 5 * 5 * 5 * 5,
                        5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
                        5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
                        5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
                        5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
                        5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5
                };
                if (exp == 0) return *this;
                for (; exp >= 27; exp -= 27) *this *= RAPIDJSON_UINT64_C2(0X6765C793, 0XFA10079D); // 5^27
                for (; exp >= 13; exp -= 13) *this *= static_cast<uint32_t>(1220703125u); // 5^13
                if (exp > 0) *this *= kPow5[exp - 1];
                return *this;
            }

            // Compute absolute difference of this and rhs.
            // Assume this != rhs
            bool Difference(const BigInteger &rhs, BigInteger *out) const {
                int cmp = Compare(rhs);
                RAPIDJSON_ASSERT(cmp != 0);
                const BigInteger *a, *b;  // Makes a > b
                bool ret;
                if (cmp < 0) {
                    a = &rhs;
                    b = this;
                    ret = true;
                }
                else {
                    a = this;
                    b = &rhs;
                    ret = false;
                }

                Type borrow = 0;
                for (size_t i = 0; i < a->count_; i++) {
                    Type d = a->digits_[i] - borrow;
                    if (i < b->count_)
                        d -= b->digits_[i];
                    borrow = (d > a->digits_[i]) ? 1 : 0;
                    out->digits_[i] = d;
                    if (d != 0)
                        out->count_ = i + 1;
                }

                return ret;
            }

            int Compare(const BigInteger &rhs) const {
                if (count_ != rhs.count_)
                    return count_ < rhs.count_ ? -1 : 1;

                for (size_t i = count_; i-- > 0;)
                    if (digits_[i] != rhs.digits_[i])
                        return digits_[i] < rhs.digits_[i] ? -1 : 1;

                return 0;
            }

            size_t GetCount() const { return count_; }

            Type GetDigit(size_t index) const {
                RAPIDJSON_ASSERT(index < count_);
                return digits_[index];
            }

            bool IsZero() const { return count_ == 1 && digits_[0] == 0; }

        private:
            void AppendDecimal64(const char *begin, const char *end) {
                uint64_t u = ParseUint64(begin, end);
                if (IsZero())
                    *this = u;
                else {
                    unsigned exp = static_cast<unsigned>(end - begin);
                    (MultiplyPow5(exp) <<= exp) += u;   // *this = *this * 10^exp + u
                }
            }

            void PushBack(Type digit) {
                RAPIDJSON_ASSERT(count_ < kCapacity);
                digits_[count_++] = digit;
            }

            static uint64_t ParseUint64(const char *begin, const char *end) {
                uint64_t r = 0;
                for (const char *p = begin; p != end; ++p) {
                    RAPIDJSON_ASSERT(*p >= '0' && *p <= '9');
                    r = r * 10u + static_cast<unsigned>(*p - '0');
                }
                return r;
            }

            // Assume a * b + k < 2^128
            static uint64_t MulAdd64(uint64_t a, uint64_t b, uint64_t k, uint64_t *outHigh) {
#if defined(_MSC_VER) && defined(_M_AMD64)
                uint64_t low = _umul128(a, b, outHigh) + k;
                if (low < k)
                    (*outHigh)++;
                return low;
#elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) && defined(__x86_64__)
                __extension__ typedef unsigned __int128 uint128;
                uint128 p = static_cast<uint128>(a) * static_cast<uint128>(b);
                p += k;
                *outHigh = static_cast<uint64_t>(p >> 64);
                return static_cast<uint64_t>(p);
#else
                const uint64_t a0 = a & 0xFFFFFFFF, a1 = a >> 32, b0 = b & 0xFFFFFFFF, b1 = b >> 32;
                uint64_t x0 = a0 * b0, x1 = a0 * b1, x2 = a1 * b0, x3 = a1 * b1;
                x1 += (x0 >> 32); // can't give carry
                x1 += x2;
                if (x1 < x2)
                    x3 += (static_cast<uint64_t>(1) << 32);
                uint64_t lo = (x1 << 32) + (x0 & 0xFFFFFFFF);
                uint64_t hi = x3 + (x1 >> 32);

                lo += k;
                if (lo < k)
                    hi++;
                *outHigh = hi;
                return lo;
#endif
            }

            static const size_t kBitCount = 3328;  // 64bit * 54 > 10^1000
            static const size_t kCapacity = kBitCount / sizeof(Type);
            static const size_t kTypeBit = sizeof(Type) * 8;

            Type digits_[kCapacity];
            size_t count_;
        };

    } // namespace internal
RAPIDJSON_NAMESPACE_END

#endif // RAPIDJSON_BIGINTEGER_H_
